The sum of the coefficients of all even degree terms in x in the expansion of `(x+sqrt(x^(3)-1))^(6)+(x-sqrt(x^(3)-1))^(6) , (xlt1)` is equal to 4k. The value of k is ________

Explanation

To find the sum of the coefficients of all even degree terms in the expansion of \((x + \sqrt{x^3 - 1})^6 + (x - \sqrt{x^3 - 1})^6\), we can follow these steps:

### Step 1: Expand the expressions
We can use the binomial theorem to expand both expressions:

\[ (x + \sqrt{x^3 - 1})^6 = \sum_{k=0}^{6} \binom{6}{k} x^{6-k} (\sqrt{x^3 - 1})^k \]
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